data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain organism begins with 5 cells. Each cell splits and becomes three cells at the end of three days. At the end of another three days, every cell of the organism splits and... | math | {
"ground_truth": "135",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Bob play a similar game with a basketball. On each turn, if Alice has the ball, there is a 2/3 chance that she will toss it to Bob and a 1/3 chance that she will keep t... | math | {
"ground_truth": "\\frac{5}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive integer $n$ , consider a triangular array with entries $a_{ij}$ where $i$ ranges from $1$ to $n$ and $j$ ranges from $1$ to $n-i+1$ . The entries o... | math | {
"ground_truth": "2^{\\left\\lceil \\frac{n}{2} \\right\\rceil}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that John places six ounces of coffee into a ten-ounce cup and four ounces of milk into another ten-ounce cup, he then pours three ounces of coffee from the first cup to th... | math | {
"ground_truth": "\\frac{16}{49}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\tan (x+\\frac{\\pi }{4})$, find the monotonic increasing interval of this function.",
"role": "user"
}
] | math | {
"ground_truth": "(k\\pi -\\frac{3\\pi }{4},k\\pi +\\frac{\\pi }{4})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$$ \\frac{1}{1\\cdot2}+\\frac{1}{2\\cdot3}+\\frac{1}{3\\cdot4}+\\dots+\\frac{1}{2014\\cdot2015}=\\frac{m}{n}, $$ where $\\frac{m}{n}$ is irreducible. \na) Find $m+n.$ b) Fin... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest digit $x$ such that $52x4$ is divisible by 7.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hyperbola \\(\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1(a,b>0)\\) with left and right foci as \\(F_{1}\\) and \\(F_{2}\\), a line passing through \\(F_{2}\\) with an i... | math | {
"ground_truth": "\\sqrt{2}+1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two less than the reciprocal of a particular number is $\\frac{5}{4}$. What is the original number expressed as a common fraction?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On hypotenuse $AB$ of a right triangle $ABC$, a second right triangle $ABD$ is constructed with hypotenuse $AB$. If $\\overline{BC}=3$, $\\overline{AC}=a$, and $\\overline{AD}=4$... | math | {
"ground_truth": "\\sqrt{a^2 - 7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $300$ participants to a mathematics competition. After the competition some of the contestants play some games of chess. Each two contestants play at most one game ag... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\(\\frac{\\log _{2}\\left(x^{3}+3 x^{2}+2 x-1\\right)}{\\log _{2}\\left(x^{3}+2 x^{2}-3 x+5\\right)}=\\log _{2 x} x+\\log _{2 x} 2\\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the country of North Southland, statisticians estimate that there is a baby born every 5 hours and two deaths every day. Determine the number of people added to the population... | math | {
"ground_truth": "1100",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $ a\\in\\mathbb{R}$ , let $ M(a)$ be the maximum value of the function $ f(x)\\equal{}\\int_{0}^{\\pi}\\sin (x\\minus{}t)\\sin (2t\\minus{}a)\\ dt$ .\r\n\r\nEvaluate $ \... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A quadruple $(a,b,c,d)$ of distinct integers is said to be $balanced$ if $a+c=b+d$ . Let $\\mathcal{S}$ be any set of quadruples $(a,b,c,d)$ where $1 \\leqslant a<b<d... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of all the solutions of \\( x = |2x - |50-2x|| \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{170}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$n>1$ is an integer. The first $n$ primes are $p_1=2,p_2=3,\\dotsc, p_n$ . Set $A=p_1^{p_1}p_2^{p_2}...p_n^{p_n}$ .\nFind all positive integers $x$ , such that $\\dfrac Ax... | math | {
"ground_truth": "x = \\prod_{i=1}^n p_i",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular carpet measures 12 feet by 18 feet. It contains a central rectangle shaded area and twelve smaller shaded squares evenly distributed around it. If the ratio $18:\\t... | math | {
"ground_truth": "114.75 \\text{ square feet}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The integers $r$ and $k$ are randomly selected, where $-5 < r < 8$ and $1 < k < 10$. What is the probability that the division $r \\div k$ results in an integer value with the ad... | math | {
"ground_truth": "\\frac{5}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Inside an equilateral triangle $DEF$, there is a point $Q$ such that $QD = 9$, $QE = 12$, and $QF=15$. What is the area of triangle $DEF$ to the nearest integer?\n- A) 85\n- B) 9... | math | {
"ground_truth": "\\textbf{(C)}\\ 97",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the range of the real number \\( a \\) such that the inequality\n$$\n\\sin 2 \\theta-(2 \\sqrt{2}+\\sqrt{2} a) \\cdot \\sin \\left(\\theta+\\frac{\\pi}{4}\\right)-\\frac{2 \... | math | {
"ground_truth": "a > 3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the values of $p$ and $q$ such that $\\log p + \\log q = \\log (p + 2q)$.\n**A)** $p = \\frac{2q}{q+1}$ \n**B)** $p = \\frac{2q^2}{q+1}$ \n**C)** $p = \\frac{2q}{q-1}... | math | {
"ground_truth": "p = \\frac{2q}{q-1}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square with a side of 75 mm was cut by two parallel cuts into three rectangles. It turned out that the perimeter of one of these rectangles is half the sum of the perimeters of... | math | {
"ground_truth": "20 \\ \\text{cm}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the result of $\\frac{2}{5} - \\frac{1}{10} + \\frac{3}{5}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{10}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the sum of two numbers is 0 and their product is -1, find the sum of their cubes.\nA) 3\nB) -1\nC) 0\nD) -3",
"role": "user"
}
] | math | {
"ground_truth": "C) 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the coordinates of point $A$ which is equidistant from points $B$ and $C$.\n\n$A(0 ; 0 ; z)$\n\n$B(-1 ;-1 ;-6)$\n\n$C(2 ; 3 ; 5)$",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a_n = \\begin{cases} \\frac{2^{n+1}}{2^n+1}, & 1 \\leq n < 10000 \\\\ \\frac{(n+1)^2}{n^2+1}, & n \\geq 10000 \\end{cases}$, where $n \\in \\mathbb{N}^*$, then $\\lim_{n \... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of $\\int_0^1 \\{\\sqrt{x}-(a+bx)\\}^2dx$ .\n\nPlease solve the problem without using partial differentiation for those who don't learn it.\n\n1961 Waseda... | math | {
"ground_truth": "\\frac{1}{450}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "p1. Known points $A (-1.2)$ , $B (0,2)$ , $C (3,0)$ , and $D (3, -1)$ as seen in the following picture.\n Determine the measure of the angle $AOD$ .\n![Image](https://cdn.... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of $a$ to $b$ is $5:4$, the ratio of $c$ to $d$ is $4:3$, and the ratio of $d$ to $b$ is $1:7$. Find the ratio of $a$ to $c$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{105}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the first term of a geometric sequence be $\\frac{1}{2}$, and let the second term be $10$. What is the smallest $n$ for which the $n$th term of the sequence is divisible by f... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the probability that if the digits $0,1,2, \\ldots, 9$ are placed in random order into the empty places in the row of digits\n\n$$\n5-383-8-2-936-5-8-203-9-3-76\n$$\n\nthe r... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the perimeter, in cm, of quadrilateral $EFGH$ if $\\overline{EF} \\perp \\overline{FG}$, $\\overline{HG} \\perp \\overline{FG}$, $EF=12$ cm, $HG=3$ cm, and $FG=16$ cm?",
... | math | {
"ground_truth": "31 + \\sqrt{337} \\text{ cm}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct the image of the parallelepiped \\(A B C D A_1 B_1 C_1 D_1\\), given the images of points \\(A\\), \\(C\\), \\(B_1\\), and \\(D_1\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Constructed parallelepiped} \\, ABCD A_1 B_1 C_1 D_1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Based on the definition of the derivative, find $f^{\\prime}(0)$:\n\n$$\nf(x)=\\left\\{\\begin{array}{c}\n\\frac{2^{\\operatorname{tg} x}-2^{\\sin x}}{x^{2}}, x \\neq 0 \\\\\n0, ... | math | {
"ground_truth": "\\ln \\sqrt{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Emily drove the first quarter of her journey on a windy road and the remaining one-sixth on a country lane. If she also drove the next 24 miles on a highway, calculate the total ... | math | {
"ground_truth": "\\frac{288}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Line $L$ is the intersection of the planes $2x - y + 2z = 4$ and $3x + 4y - z = 6$. A plane $P$, different from both these planes, contains line $L$, and has a distance of $\\fra... | math | {
"ground_truth": "x + 63y - 35z - 34 = 0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are nine dots arranged in a $3\\times3$ grid, calculate the number of distinct triangles that can be drawn using three of these dots as vertices.",
"role": "... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ABCD$ is a rectangle acting as the base of pyramid $P$, with dimensions $AB = 15$ and $BC = 20$. Pyramid $P$ has a height of $30$. A plane parallel to base $ABCD$ slices through... | math | {
"ground_truth": "20 \\text{ units}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x\\#y = xy - 3x$, what is the value of $(8\\#3) - (3\\#8)$?",
"role": "user"
}
] | math | {
"ground_truth": "-15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a $3 \\times 3$ symmetric real matrix $A$ , we define $f(A)$ as a $3 \\times 3$ matrix with the same eigenvectors of $A$ such that if $A$ has eigenvalues $a$ , ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute\n\\[\n\\sum_{n = 1}^\\infty \\frac{2n + 3}{n(n + 1)(n + 2)}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Matthew's current test scores of $88, 77, 82, 90, 75,$ and $85,$ and aiming to increase his average score by at least $4$ points with his next test, determine the minimum t... | math | {
"ground_truth": "110.81",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the point in the $xy$-plane that is equidistant from the points $(2,0,-1),$ $(1,-2,3),$ and $(4,2,1).$",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{11}{10}, -\\frac{21}{20}, 0\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\frac{a}{10^x-3}+\\frac{b}{10^x+4}=\\frac{3 \\cdot 10^x+4}{(10^x-3)(10^x+4)}$ is an identity for positive rational values of $x$, then find the value of $a+b$.\nA) 2\nB) $\\... | math | {
"ground_truth": "C) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many ways can one make $n$ kopecks using coins of:\n\na) 1 kopeck, 2 kopecks, and 3 kopecks?\n\nb) 1 kopeck, 2 kopecks, and 5 kopecks?",
"role": "user"
}
] | math | {
"ground_truth": "\\left\\lfloor \\frac{(n+4)^2}{20} \\right\\rfloor",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathcal E$ be an ellipse with foci $F_1$ and $F_2$ . Parabola $\\mathcal P$ , having vertex $F_1$ and focus $F_2$ , intersects $\\mathcal E$ at two points $X$... | math | {
"ground_truth": "\\frac{2 + \\sqrt{13}}{9}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area of the triangle whose vertices are the points of intersection of the curves \\(x^2 + y^2 = 16\\) and \\((x-2)^2 + 4y^2 = 36\\)?\nA) \\( \\frac{13\\sqrt{80}}{9} \... | math | {
"ground_truth": "**C**) \\( \\frac{16\\sqrt{80}}{9} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many right trapezoids \\(ABCD\\) exist, where angles \\(A\\) and \\(B\\) are right angles, \\(AD = 2\\), \\(CD = BC\\), the sides have integer lengths, and the perimeter is l... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Marie's high school has 4 times as many students as Clara's high school. Together, the schools have a total of 2500 students. Calculate the number of students in Marie's high sch... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a circle $C$ passes through two points $M(-3,3)$ and $N(1,-5)$, and the center of the circle $C$ lies on the line $2x-y-2=0$.\n\n$(1)$ Find the standard equation of the cir... | math | {
"ground_truth": "( \\frac{15}{8},+\\infty )",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The original plan was to spend 1500 yuan to buy $x$ units of product A and $y$ units of product B. Unexpectedly, the price of product A increased by 1.5 yuan per unit, and the pr... | math | {
"ground_truth": "x = 76, y = 55",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Below is a portion of the graph of a function, \\( y = F(x) \\):\n\n\\[ F(x) = \\sqrt{|x+2|} + \\frac{12}{\\pi}\\tan^{-1}(\\sqrt{|x-1|}) \\]\n\nDetermine the value of \\( F(4) \\... | math | {
"ground_truth": "\\sqrt{6} + 4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers \\( n \\) such that \\( 4n^4 + 1 \\) is a prime number.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f(x)=\\sin (x+ \\frac {π}{2})$ and $g(x)=\\cos (x- \\frac {π}{2})$, determine the correct conclusion(s) from the options below.\n\n(1) The smallest positive period of the ... | math | {
"ground_truth": "(1), (2), (4)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(a\\) copies of a right-angled isosceles triangle with hypotenuse \\(\\sqrt{2} \\, \\mathrm{cm}\\) can be assembled to form a trapezium with perimeter equal to \\(b \\, \\ma... | math | {
"ground_truth": "4 + 2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of distinct monic quadratic polynomials with integer coefficients that have at least one root, all their roots being powers of the number 7 with non-negative inte... | math | {
"ground_truth": "4760",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two bodies simultaneously start from the same point: one with a velocity \\( v_{1} = 5t \\, \\text{m/s} \\), and the other with a velocity \\( v_{2} = 3t^{2} \\, \\text{m/s} \\).... | math | {
"ground_truth": "7000 \\ \\mathrm{m}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ABC$ has vertices $A(3, -2)$, $B(-1, 1)$, and $C(5, 4)$. The triangle is reflected over the $y$-axis to form triangle $A'B'C'$. What is the length of the segment drawn ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The toy factory produces wireframe cubes, with small multicolored balls placed at the vertices. According to the standard, each cube must use balls of all eight colors (white and... | math | {
"ground_truth": "1680",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\( f \\) is a continuous real-valued function such that \\( f(x + y) = f(x) f(y) \\) for all real \\( x \\) and \\( y \\). If \\( f(2) = 5 \\), find \\( f(5) \\).",
"role": ... | math | {
"ground_truth": "25\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of $s$ when the quadratic equation $$16x^2 + 32x - 512 = 0$$ is solved by completing the square, resulting in an equation of the form $$(x + r)^2 = s.$$",
... | math | {
"ground_truth": "s = 33",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least possible cardinality of a set $A$ of natural numbers, the smallest and greatest of which are $1$ and $100$ , and having the property that every element of $A... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a five-digit number $n$ with quotient $q$ and remainder $r$ when divided by 100, determine the number of values of $n$ for which $q+r$ is divisible by $11$.",
"role": "us... | math | {
"ground_truth": "9000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the range of the function \\[ f(x) = \\frac{x+1}{x^2 - 2x + 2}, \\] where \\( x \\) is any real number.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[\\frac{1 - \\sqrt{2}}{2}, \\frac{1 + \\sqrt{2}}{2}\\right]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality $x^{2}-ax-a+1\\geqslant 0$ has solutions for $x\\in \\left[0,3\\right]$, the range of real number $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, \\frac{5}{2}]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Tourists arrived at a campsite. For lunch, each of them ate half a can of soup, a third of a can of stew, and a quarter of a can of beans. In total, they consumed 39 cans of food... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given ${(1-2x)}^{2023}={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+⋅⋅⋅+{a}_{2023}{x}^{2023}$, find the sum of the coefficients of all terms in the expansion.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the product of all $x$ values for which the expression $\\frac{x^2+3x+2}{x^2+3x-4}$ is undefined.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider two arithmetic sequences: $3, 8, 13, \\ldots$ and $10, 19, 28, \\ldots$. If $S$ is the union of the first $3000$ terms from each sequence, how many distinct numbers are ... | math | {
"ground_truth": "B) 5667",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A unicorn is tethered by a 20-foot silver rope to the base of a magician's cylindrical tower whose radius is 8 feet. The rope is attached to the tower at ground level and to the ... | math | {
"ground_truth": "813",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nair and Yuli play the following game: $1.$ There is a coin to be moved along a horizontal array with $203$ cells. $2.$ At the beginning, the coin is at the first cell, count... | math | {
"ground_truth": "4k + 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $3x - 2y > 4x + 1$ and $2x + 3y < 5y - 2$, solve for the relationship between $x$ and $y$.\nA) $x < 1 - y$\nB) $x > 1 - y$\nC) $x < -1 - 2y$\nD) $x > -1 - 2y$\nE) $x > -1 - 2y... | math | {
"ground_truth": "x < 1 - y",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mike is 30 years younger than his mom. The sum of their ages is 70 years. In 5 years, what will be the sum of their ages?",
"role": "user"
}
] | math | {
"ground_truth": "80",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:<br/>$(1)15+(-6)+3-(-4)$;<br/>$(2)8-{2}^{3}÷\\frac{4}{9}×{(-\\frac{2}{3})}^{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(n) =\\left\\{\\begin{matrix}\\log_{8}{n}, &\\text{if }\\log_{8}{n}\\text{ is rational,}\\\\ 0, &\\text{otherwise,}\\end{matrix}\\right.$ evaluate the summat... | math | {
"ground_truth": "\\frac{55}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of ways to arrange the letters of the word PERMUTATION.",
"role": "user"
}
] | math | {
"ground_truth": "9,\\!979,\\!200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x, y$ and $z$ be consecutive integers such that\n\\[\\frac 1x+\\frac 1y+\\frac 1z >\\frac{1}{45}.\\]\nFind the maximum value of $x + y + z$ .",
"role": "user"
}
] | math | {
"ground_truth": "402",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the last digit of the decimal expansion of $\\frac{1}{2^{10} \\times 3^{10}}$?",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\begin{cases}x, & x\\geqslant a, \\\\ x^3-3x, & x < a.\\end{cases}$ If the function $g(x)=2f(x)-ax$ has exactly $2$ different zeros, then the range of t... | math | {
"ground_truth": "\\left(- \\frac{3}{2},2\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Plusses and minuses are inserted in the expression \\[\\pm 1 \\pm 2 \\pm 3 \\dots \\pm 2016\\] such that when evaluated the result is divisible by 2017. Let there be $N$ ways f... | math | {
"ground_truth": "256",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the domain of the function $g(x) = \\tan(\\arcsin(x^3))$.",
"role": "user"
}
] | math | {
"ground_truth": "(-1, 1)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Within a group of $ 2009$ people, every two people has exactly one common friend. Find the least value of the difference between the person with maximum number of friends and t... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the complex number $z=-1-i$ (where $i$ is the imaginary unit), and its complex conjugate $\\overline{z}$, find the value of $|(1-z)\\cdot\\overline{z}|$.",
"role": "use... | math | {
"ground_truth": "\\sqrt{10}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the number of tuples \\(\\left(a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\\right)\\) of (not necessarily positive) integers such that \\(a_{i} \\leq i\\) for all \\(0 \\leq... | math | {
"ground_truth": "2002",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fly is flying inside a regular tetrahedron with edge length \\( a \\). What is the minimum distance it must travel in order to visit each face and return to the starting point?... | math | {
"ground_truth": "\\frac{4\\sqrt{2}}{\\sqrt{3}} a \\text{ or } \\frac{4\\sqrt{6}}{3} a",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two spheres of one radius and two of another are arranged such that each sphere touches three others and a given plane. Find the ratio of the radii of the larger sphere to the sm... | math | {
"ground_truth": "2 + \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers \\( n > 0 \\) such that \\( n^2 \\mid 2^n + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "1 \\text{ et } 3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f$ be the quadratic function with leading coefficient $1$ whose graph is tangent to that of the lines $y=-5x+6$ and $y=x-1$ . The sum of the coefficients of $f$ is... | math | {
"ground_truth": "2509",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. Simplify and evaluate the expression: $\\log_{\\frac{1}{3}} \\sqrt{27} + \\lg 25 + \\lg 4 + 7^{-\\log_{7} 2} + (-0.98)^0$\n2. Given a point $P(\\sqrt{2}, -\\sqrt{6})$ on the t... | math | {
"ground_truth": "\\frac{-\\sqrt{3} - 1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two adjacent sides of a rhombus form a $45$-degree angle. If each side of the rhombus measures $4$ cm, what is the area of the rhombus, in square centimeters?",
"role": "user... | math | {
"ground_truth": "4\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lenka is thinking of two two-digit numbers. One number has both digits even, and the other number has both digits odd. When she adds these two numbers, the result is again a two-... | math | {
"ground_truth": "\\{24, 39\\}, \\{42, 39\\}, \\{48, 39\\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a rectangle with $AB = 6$ and $BC = 6 \\sqrt 3$ . We construct four semicircles $\\omega_1$ , $\\omega_2$ , $\\omega_3$ , $\\omega_4$ whose diameters are... | math | {
"ground_truth": "243",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A perfect square integer is written in base 7 as $ac4b$, where $a \\ne 0$. Express the base 7 number in terms of $a$ and $b$, and then determine the possible values of $b$ for wh... | math | {
"ground_truth": "0, 1, 4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the six-digit integer $4A8,\\!851$, what is the smallest digit $A$ so that the six-digit integer will be divisible by 3?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fun \"Sports Day\" organized by a certain school for seventh graders has a total of five competition events. Each class participates in all events, and it is stipulated that on... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Real numbers between 0 and 1, inclusive, are chosen as follows: A fair coin is flipped three times. If the first two flips are heads, then the number is 0 if the third flip is he... | math | {
"ground_truth": "\\textbf{(B) } \\frac{423}{1024}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the shown diagram, segment $CD$ is parallel to segment $WX$. If $CX = 30$ units, $DP = 15$ units, and $PW = 45$ units, find the length of segment $PX$. Diagram:\n[asy]\nimport... | math | {
"ground_truth": "22.5 \\text{ units}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest integer $x$ such that $\\frac{x}{4} + \\frac{3}{7} > \\frac{4}{3}$?\n\n---",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the integer $n$, $0 \\le n \\le 12$, such that \\[n \\equiv 123456 \\pmod{11}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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